22,074 research outputs found
Islands in the Gap: Intertwined Transport and Localization in Structurally Complex Materials
Localized waves in disordered one-dimensional materials have been studied for
decades, including white-noise and correlated disorder, as well as
quasi-periodic disorder. How these wave phenomena relate to those in
crystalline (periodic ordered) materials---arguably the better understood
setting---has been a mystery ever since Anderson discovered disorder-induced
localization. Nonetheless, together these revolutionized materials science and
technology and led to new physics far beyond the solid state. We introduce a
broad family of structurally complex materials---chaotic crystals---that
interpolate between these organizational extremes---systematically spanning
periodic structures and random disorder. Within the family one can tune the
degree of disorder to sweep through an intermediate structurally disordered
region between two periodic lattices. This reveals new transport and
localization phenomena reflected in a rich array of energy-dependent
localization degree and density of states. In particular, strong localization
is observed even with a very low degree of disorder. Moreover, markedly
enhanced localization and delocalization coexist in a very narrow range of
energies. Most notably, beyond the simply smoothed bands found in previous
disorder studies, islands of transport emerge in band gaps and sharp band
boundaries persist in the presence of substantial disorder. Finally, the family
of materials comes with rather direct specifications of how to assemble the
requisite material organizations.Comment: 7 pages, 3 figures, supplementary material;
http://csc.ucdavis.edu/~cmg/compmech/pubs/talisdm.ht
Non-commutative p-adic L-functions for supersingular primes
Let E/Q be an elliptic curve with good supersingular reduction at p with
a_p(E)=0. We give a conjecture on the existence of analytic plus and minus
p-adic L-functions of E over the Zp-cyclotomic extension of a finite Galois
extension of Q where p is unramified. Under some technical conditions, we adopt
the method of Bouganis and Venjakob for p-ordinary CM elliptic curves to
construct such functions for a particular non-abelian extension.Comment: 13 pages; some minor corrections; to appear in International Journal
of Number Theor
Glassy Dynamics in a Frustrated Spin System: Role of Defects
In an effort to understand the glass transition, the kinetics of a spin model
with frustration but no quenched randomness has been analyzed. The
phenomenology of the spin model is remarkably similiar to that of structural
glasses. Analysis of the model suggests that defects play a major role in
dictating the dynamics as the glass transition is approached.Comment: 9 pages, 5 figures, accepted in J. Phys.: Condensed Matter,
proceedings of the Trieste workshop on "Unifying Concepts in Glass Physics
A new approach to upscaling fracture network models while preserving geostatistical and geomechanical characteristics
A new approach to upscaling two-dimensional fracture network models is proposed for preserving geostatistical and geomechanical characteristics of a smaller-scale “source” fracture pattern. First, the scaling properties of an outcrop system are examined in terms of spatial organization, lengths, connectivity, and normal/shear displacements using fractal geometry and power law relations. The fracture pattern is observed to be nonfractal with the fractal dimension D ≈ 2, while its length distribution tends to follow a power law with the exponent 2 < a < 3. To introduce a realistic distribution of fracture aperture and shear displacement, a geomechanical model using the combined finite-discrete element method captures the response of a fractured rock sample with a domain size L = 2 m under in situ stresses. Next, a novel scheme accommodating discrete-time random walks in recursive self-referencing lattices is developed to nucleate and propagate fractures together with their stress- and scale-dependent attributes into larger domains of up to 54 m × 54 m. The advantages of this approach include preserving the nonplanarity of natural cracks, capturing the existence of long fractures, retaining the realism of variable apertures, and respecting the stress dependency of displacement-length correlations. Hydraulic behavior of multiscale growth realizations is modeled by single-phase flow simulation, where distinct permeability scaling trends are observed for different geomechanical scenarios. A transition zone is identified where flow structure shifts from extremely channeled to distributed as the network scale increases. The results of this paper have implications for upscaling network characteristics for reservoir simulation
Coordination motifs and large-scale structural organization in atomic clusters
The structure of nanoclusters is complex to describe due to their
noncrystallinity, even though bonding and packing constraints limit the local
atomic arrangements to only a few types. A computational scheme is presented to
extract coordination motifs from sample atomic configurations. The method is
based on a clustering analysis of multipole moments for atoms in the first
coodination shell. Its power to capture large-scale structural properties is
demonstrated by scanning through the ground state of the Lennard-Jones and
C clusters collected at the Cambridge Cluster Database.Comment: 6 pages, 7 figure
Spectral Representation Theory for Dielectric Behavior of Nonspherical Cell Suspensions
Recent experiments revealed that the dielectric dispersion spectrum of
fission yeast cells in a suspension was mainly composed of two sub-dispersions.
The low-frequency sub-dispersion depended on the cell length, while the
high-frequency one was independent of it. The cell shape effect was simulated
by an ellipsoidal cell model but the comparison between theory and experiment
was far from being satisfactory. Prompted by the discrepancy, we proposed the
use of spectral representation to analyze more realistic cell models. We
adopted a shell-spheroidal model to analyze the effects of the cell membrane.
It is found that the dielectric property of the cell membrane has only a minor
effect on the dispersion magnitude ratio and the characteristic frequency
ratio. We further included the effect of rotation of dipole induced by an
external electric field, and solved the dipole-rotation spheroidal model in the
spectral representation. Good agreement between theory and experiment has been
obtained.Comment: 19 pages, 5 eps figure
Spin-one ferromagnets with single-ion anisotropy in a perpendicular external field
In this paper, the conventional Holstein-Primakoff method is generalized with
the help of the characteristic angle transformation [Lei Zhou and Ruibao Tao,
J. Phys. A {\bf 27} 5599 (1994)] for the spin-one magnetic systems with
single-ion anisotropies. We find that the weakness of the conventional method
for such systems can be overcome by the new approach. Two models will be
discussed to illuminate the main idea, which are the ``easy-plane" and the
``easy-axis" spin-one ferromagnet, respectively. Comparisons show that the
current approach can give reasonable ground state properties for the magnetic
system with ``easy-plane" anisotropy though the conventional method never can,
and can give a better representation than the conventional one for the magnetic
system with ``easy-axis" anisotropy though the latter is usually believed to be
a good approximation in such case. Study of the easy-plane model shows that
there is a phase transition induced by the external field, and the
low-temperature specific heat may have a peak as the field reaches the critical
value.Comment: Using LaTex. To be published in the September 1 issue of Physical
Review B (1996). Email address: [email protected]
Identification and Estimation of Nonseparable Single-Index Models in Panel Data with Correlated Random Effects
Abstract: The identification of parameters in a nonseparable single-index models with correlated random effects is considered in the context of panel data with a fixed number of time periods. The identification assumption is based on the correlated random-effect structure: the distribution of individual effects depends on the explanatory variables only by means of their time-averages. Under this assumption, the parameters of interest are identified up to scale and could be estimated by an average derivative estimator based on the local polynomial smoothing. The rate of convergence and asymptotic distribution of the proposed estimator are derived along with a test whether pooled estimation using all available time periods is possible. Finally, a Monte Carlo study indicates that our estimator performs quite well in finite samples.
- …